Filtering in Projection-based Integrators for Improved Phase Characteristics

Projection-based integrators are effectively employed in high-precision systems with growing industrial success. By utilizing a projection operator, the resulting projection-based integrator keeps its input-output pair within a designated sector set, leading to unique freedom in control design that can be directly translated into performance benefits. This paper aims to enhance projection-based integrators by incorporating well-crafted linear filters directly into its structure, resulting in a new class of projected integrators that includes the earlier ones, such as the hybrid-integrator gain systems (HIGS), as special cases. The extra design freedom in the form of two filters in the input paths to the projection operator and the internal dynamics allows the controller to break away from the inherent limitations of a linear control design. The enhanced performance properties of the proposed structure are formally demonstrated through i) a describing function analysis, ii) mitigation of the gain-loss problem (occurring in, e.g., HIGS), and iii) numerical case studies showcasing improved time-domain properties. The describing function analysis is supported by rigorously showing incremental properties of the new filtered projection-based integrators, thereby guaranteeing the steady-state responses to be unique and asymptotically stable.